Question

the circumference of the base of a 10m height conical tent is 44m. calculate the length of canvas used in making the text if width of canvas is 2m

Answer 1

Acc to question
CSA of cone= Area of canvas
$\pi \: rl = l \times b$
C=44m h=10m
$2 \: \pi \: r = 44$
2×22/7×r=44
r=44×7/22×2=7m
$l \: = \: \: \sqrt{ {10}^{2} + {7}^{2} }$
$l \: = \sqrt{ {h}^{2} + {r}^{2} } \:$
$l = \: \sqrt{100 + 49 }$
$l = \sqrt{149} = 12.2$
$csa = \pi \: \times 7 \times 12.2$
=>CSA=22×12.2=268.4 m2
area of canvas =l×2=csa of cone
2l=268.4

$l = 268.4 \div 2 = 134.2$
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Answer 2

Given:-

• The circumference of the base of a 10m height conical tent is 44m.

To find:-

• The length of canvas .....?

Solutions:-

• Circumference of base of tent = 44m.

Circumference of circle = 2πr

2πr = 44m

r = 44 × 7 / 2 × 22

r = 7m

The vertical height of the cone is h = 10m.

Slant height, l = √r² + h²

= √7² + 10²

= √49 + 100

= √149m

Now, substituting the value of r = 7m and slant height l = √149 and using π = 22/7 in the formula of CSA.

Curved surface area = πrl

= 22/7 × 7 × √149

= 22 × √149

= 22√149

Hence, the curved surface area of the cone = 22√149m²

Now, the width of the canvas is 2m

Area of the canvas required = (width of the canvas) (length of the canvas)

Therefore,

length of the canvas = Area of the canvas/width of the canvas

= 22√149/2

= 134.27m

Hence, the length of canvas required is 134.27m